Comment by hunter2_

The tricky bit is that while it's impossible to deprive someone of their idea (i.e., commit theft of an idea), it's possible to steal someone's idea (i.e., copy it and use it illicitly), because only the word theft, but not the word steal, has that "deprive others" stipulation.

So with that in mind, circling back to whether possession occurs in such a way to make possessive language appropriate (being able to say "my data" after stealing data but not depriving the author of the data), my opinion is that the copy of the data that the author still controls is the author's data, and the copy of the data that the stealer controls is the stealer's data. It's the author's idea, but both parties separately possess the data (the data is a record of the idea).